[?] Understand Violin Plot maximum and minimum values?

Questions
,
1

Hi,

In the Violin plot, why ‘data’ showes negative values below zero? The maximum of ‘data’ is 11.48, why Violin plot exceeded 12 on the y-axis?

In[10]:= data = {8.58`, 1.85`, 4.95`, 1.36`, 1.58`, 2.06`, 5.46`, 
  11.48`, 8.86`, 9.6`, 2.37`, 5.32`, 5.71`, 5.74`, 5.34`, 5.33`, 
  5.22`, 8.13`, 8.02`, 7.58`, 7.33`, 7.98`, 6.76`, 6.29`, 7.01`, 
  5.78`, 4.12`, 2.44`, 1.97`, 3.06`, 8.46`, 7.25`, 7.38`, 6.72`, 
  7.88`, 6.61`, 2.59`, 6.76`, 6.17`, 1.15`, 5.39`, 4.44`, 6.97`, 
  7.94`, 9.3`, 7.44`}

In[13]:= {Max[data], Min[data]}

Out[13]= {11.48, 1.15}

8116Untitled.png
8116Untitled.png913×569 7.82 KB

2

This is because here a “smoothed out” distribution is shown. If you do not like this, you can change the option ChartElementFunction, e.g.:

DistributionChart[data, ChartElementFunction -> #, 
   GridLines -> {None, Automatic}] & /@ {Automatic, "Quantile", 
  "DensityQuantile", "FadingQuantile", "GlassQuantile", "Density", 
  "HistogramDensity", "LineDensity", "PointDensity"}

violin.png
violin.png578×399 10.6 KB

3

Thank you very much Henrik.

So what is the main difference between Violin plot and Density plot.?

4

DensityPlot is for plotting 2D-densities and does not has per se anything to do with statistics. Maybe this comparison helps:

Through[{Histogram, SmoothHistogram}[data, GridLines -> Automatic]]

hists.png
hists.png387×126 2.59 KB

As you see, the SmoothHistogram exceeds the MinMax values of the data, which is reasonable.
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=hists.png&userId=32203

5

Thank you very much Henrik.